A High-Frequency Model for PCB Rogowski Coils

This article proposes a high-frequency model for Rogowski coils (RCs) implemented on printed circuit boards that extends existing transmission-line (TL) models developed for wire-wound helical coils, which assume a uniform induced-voltage distribution. The model explicitly accounts for the nonuniform spatial distribution of induced-voltages along the winding and supports arbitrary bilateral terminations. This is achieved by calculating the partial mutual inductance between the primary conductor and the traces and vias of the sensor, the former modeled as TL segments and the latter treated as lumped voltage sources. Three relevant cases are studied: a critically damped coil, a bimatched coil, and a self-integrating coil. Analytical expressions are obtained for each case, and a comparison with classical models shows equivalence for simplified scenarios that assume uniform mutual inductance for the first two cases under appropriate conditions. Moreover, the new model reveals bandwidth limitations for the self-integrating case and predicts the frequency response of the bimatched termination, the latter a sensor configuration not fully covered to date. Experimental validation is conducted on representative samples of the modeled current sensor using a custom-made test fixture, yielding an excellent agreement between the measured and predicted transfer impedance.